Analog signals are generally translated into their digital form by applying them to analog-to-digital converters, hereinafter referred to as A/D's, before any computation or signal processing is performed. The A/D's sample the amplitude of the analog signal at intervals of t.sub.0 seconds and produce digital words that represent the closest amplitude to the actual amplitude of each sample that can be attained with the number of bits used by the converter. Any difference between the actual amplitude of the sample of the analog wave and the amplitude represented by digital words derived from it is known as "digitization noise".
The highest frequency of the analog signal that can be accurately represented by such a sampling process is known as the "Nyquist frequency" and is equal to one-half the sampling frequency. If the analog signal is permitted to include higher frequencies, they can heterodyne with the sampling frequency and its harmonics to produce signals lying below the Nyquist frequency and therefore within the signal frequencies of interest. This is known as "aliasing". In order to prevent this from occurring, it has been customary to pass the analog signal through a low pass filter having a cut-off at or below the Nyquist frequency, but the sharper the cut-off, the greater the phase distortion. For this reason, it would be desirable to avoid the use of an analog filter.
In many applications, interference from power lines, at 50 Hz or 60 Hz, as the case may be, can introduce severe aliasing effects. Notch filters can be used to attenuate these frequencies in the analog signal prior to its application to an A/D converter, but they also introduce troublesome errors in phase.